What is the derivative of (4ln(x+2))/(x^2) ?

The derivative of (4ln(x+2))/(x^2) is (4(x-2ln(x+2)(x+2)))/(x^3(x+2))

What is the first derivative of (4ln(x+2))/(x^2) ?

The first derivative of (4ln(x+2))/(x^2) is (4(x-2ln(x+2)(x+2)))/(x^3(x+2))

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derivative of

\frac{4 ln ( x + 2 )}{x ^{2}}

\frac{4 ( x - 2 ln ( x + 2 ) ( x + 2 ) )}{x ^{3} ( x + 2 )}

Solution steps

\frac{d}{d x} (\frac{4 ln ( x + 2 )}{x ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (\frac{ln ( x + 2 )}{x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 4 \cdot \frac{\frac{d}{d x} ( ln ( x + 2 ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ln ( x + 2 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (ln (x + 2)) = \frac{1}{x + 2}

\frac{d}{d x} (x^{2}) = 2 x

= 4 \cdot \frac{\frac{1}{x + 2} x ^{2} - 2 x ln ( x + 2 )}{( x ^{2} ) ^{2}}

Simplify

4 \cdot \frac{\frac{1}{x + 2} x ^{2} - 2 x ln ( x + 2 )}{( x ^{2} ) ^{2}} : \frac{4 ( x - 2 ln ( x + 2 ) ( x + 2 ) )}{x ^{3} ( x + 2 )}

= \frac{4 ( x - 2 ln ( x + 2 ) ( x + 2 ) )}{x ^{3} ( x + 2 )}

What is the derivative of (4ln(x+2))/(x^2) ?
The derivative of (4ln(x+2))/(x^2) is (4(x-2ln(x+2)(x+2)))/(x^3(x+2))
What is the first derivative of (4ln(x+2))/(x^2) ?
The first derivative of (4ln(x+2))/(x^2) is (4(x-2ln(x+2)(x+2)))/(x^3(x+2))